Efficient Tests for Normality, Homoscedasticity and Serial Independence of Regression Residuals

‘Classical regression analysis’ assumes the normality (N), homoscedasticity (H) and serial independence (I) of regression residuals. Violation of the normality assumption may lead the investigator to inaccurate inferential statements. Recently, tests for normality have been derived for the case of homoscedastic serially independent (HZ) residuals [e.g., White and Macdonald (1980)]. Similarly, the effects of violation of the homoscedasticity assumption have been studied and tests for this have been derived for the case of normally distributed serially independent (NZ) residuals [e.g., Breusch and Pagan (1979)]. Additionally, the consequences of violation of the assumption of serial independence have been analyzed and tests for this have been derived for the case on normally distributed homoscedastic (NH) residuals [e.g., Durbin and Watson (1950) and Breusch (1978)]. The appropriateness of these and other ‘one-directional tests’ (i.e., tests for either N or H or Z) may depend strongly on the validity of the conditions under which these were derived (e.g., we have found that the power of our normality test-see section 2 -may be seriously affected by the presence of serial correlation). In general, it is thought that these conditions should be tested rather than assuming their validity from the start. In this paper we suggest an